It’s surprising that there has not yet been a “rubbish art” headline to greet the Kurt Schwitters show that opens at Tate Britain next week. This is perhaps surprising, because his working material was, literally, rubbish – old news cuttings, bus tickets, sweet wrappings, chicken wire, pram wheels or tin cans. He even coined a term for it: “Merz”, in itself a meaningless fragment of the word “kommerz” but, in his world, a new direction for art in which all materials were valid for artistic purposes.

In 1918, everything had collapsed in Germany, and Schwitters, then an undistinguished follower of modern trends in art, decided that, as in society, “new things had to be made out of the fragments. Thrift compelled me to take what I could find because we were an impoverished country. It is quite possible to cry out with refuse, and I did this by gluing and nailing it together.”

Unlike Picasso and Juan Gris, who used collage to explore ideas for their paintings, Schwitters made the collage an art work in its own right and became a leading member of the avant-garde Dadaist and constructivist movements in Europe. He was not, though, appreciated by the Nazis, and was included in several “degenerate art” exhibitions. In 1937, threatened with interrogation by the Gestapo, he emigrated to Norway. He was only able to take his work out of Germany because customs deemed it worthless rubbish.

When the Germans invaded Norway, Schwitters packed his bags again, for Britain, where he was immediately interned, but continued to work. Sales of his “merz” art, however, were rare. Although he was recognised as a prominent figure in the European avant-garde, he had to make conventional portraits, still lives and landscapes, which he sold for a few pounds or less, to survive. Having been relatively well-off in Germany, where his family owned property, he died in Britain, aged 60, in 1948, a penniless exile.

Behind him, he left more than 3,000 works, which his son, Ernst, set about promoting with the help of the Marlborough Gallery in London and the Galerie Gmurzynska in Cologne. The task was made easier by Schwitters’s acknowledged, widespread influence. He was responsible for legitimising the use of rubbish in art for generations of artists, from Robert Rauschenberg and Jasper Johns to Rachel Whiteread and Damien Hirst.

Rauschenberg first saw Schwitters’s work in 1952, commenting that he thought the show had been made “solely for me”. “Everyone was talking about Schwitters at that time,” he said. Hirst discovered Schwitters when a student at Leeds in the early 1980s. “I love Schwitters,” he told Hans-Ulrich Obrist in 2006. “In everything I’ve ever done, there’s an element of Schwitters.”

This is not the first time that Tate has celebrated Schwitters. In 1985, it focused on the earlier, more ordered and sophisticated work on which his reputation was based, and now concentrates on the slightly cruder, later work made in Britain. In market terms, the earlier works have always been the most sought-after and have become rare, says Mathias Rastorfer of the Galerie Gmurzynska. A tiny, 5in by 4in, 1920 collage, Merz.80 (pictured) in the new show was bought at Christie’s in 2009 for £217,250 – four times the lower estimate. The record for Schwitters was set last summer when a German collector bought a larger 1919 relief painting for £1.3 million.

Bidding against him, significantly, was a collector of post-1945 art who saw Schwitters as a vital link between early and later 20th-century avant-garde art. This interest from contemporary art collectors is what is driving the Schwitters market now, say experts, and it’s affecting values for the later works too. The new Tate exhibition includes the two highest-selling works at auction from the final English period: Dancer, 1943, a painted sculpture made from plaster and animal bone that sold in Cologne in 2011 for nearly £500,000, and the 1946 Heavy Relief, which sold at Christie’s last year for £691,000, both far above estimates.

The first selling exhibition in London for 30 years is being staged by the Bernard Jacobson gallery in Cork Street, where some 20 works from the 1920s and 1940s will be priced from $250,000 (£157,000) to $450,000 (£284,000). Among them are paintings and collages from an exhibition in London in 1944, when they were priced from 15 to 40 guineas and only one of the 40 exhibits found a buyer.